A new theory was developed to compute the propagation of the pressure wave in a branching system. The theory includes cross sectional area and stiffness variation, viscous and viscoelastic effects, and side branch flow. The theory was then used in an analytical model of the brachial artery system which can reproduce the phasic pressure waveforms as measured in normal and hypertensive subjects. Particular emphasis was directed toward an understanding of the genesis of the peripheral dicrotic wave, and its modulation by vasoactive drugs.